 
Summary: Phase transitions in scalefree neural networks: Departure from the standard meanfield
universality class
Maximino Aldana* and Hernán Larralde
Centro de Ciencias Físicas, UNAM, Apartado Postal 483, Codigo Postal 62251, Cuernavaca, Morelos, Mexico
(Received 25 July 2004; published 22 December 2004)
We investigate the nature of the phase transition from an ordered to a disordered state that occurs in a family
of neural network models with noise. These models are closely related to the majority voter model, where a
ferromagneticlike interaction between the elements prevails. Each member of the family is distinguished by the
network topology, which is determined by the probability distribution of the number of incoming links. We
show that for homogeneous random topologies, the phase transition belongs to the standard meanfield uni
versality class, characterized by the order parameter exponent =1/2. However, for scalefree networks we
obtain phase transition exponents ranging from 1/2 to infinity. Furthermore, we show the existence of a phase
transition even for values of the scalefree exponent in the interval (1.5,2], where the average network con
nectivity diverges.
DOI: 10.1103/PhysRevE.70.066130 PACS number(s): 89.75.Hc, 84.35. i, 02.50.Ey, 05.45. a
I. INTRODUCTION
To determine the relationship between the topology of a
complex network and its dynamical behavior has become a
challenge in current scientific research. In the past few years
there has been a great amount of work to find out the struc
